What mistakes do students make with Measurements and uncertainties?

Adding absolute uncertainties for multiplication or division. You must add percentage uncertainties instead. Forgetting to multiply the percentage uncertainty by the power when raising to a power. Mixing absolute and percentage uncertainties without converting. Convert to a consistent form before combining.

What are the exam tips for Measurements and uncertainties in Physics OCR A-Level?

Write down the rule you are using before substituting numbers to avoid mixing rules. Convert all uncertainties to the same type (absolute or percentage) before combining. For powers, remember to multiply the percentage uncertainty by the exponent. Check that the final uncertainty has the same units as the quantity if absolute, or is a percentage if percentage.

OCR · A-Level · Physics

Course version: H556 · Version from Sept 2015

(c) absolute and percentage uncertainties when data are combined by…

Full specification wording

Measurements and uncertainties: (c) absolute and percentage uncertainties when data are combined by addition, subtraction, multiplication, division and raising to powers

When combining measurements, uncertainties propagate.

Checked against the OCR H556 specification (opens in a new tab) on 10 November 2026.

Point 3 of 4

Study notes

From the checked teaching notes for this specification point.

The idea

What earns the marks

For addition and subtraction, absolute uncertainties add.
For multiplication and division, percentage uncertainties add.
For raising to a power, percentage uncertainty is multiplied by the power.
Percentage uncertainty = (absolute uncertainty / measured value) × 100%.
Final uncertainty should be expressed in the form requested, either absolute or percentage.

Common mistakes and how to put them right

Adding absolute uncertainties for multiplication or division.
Put it right: You must add percentage uncertainties instead.
Forgetting to multiply the percentage uncertainty by the power when raising to a power.
Mixing absolute and percentage uncertainties without converting.
Put it right: Convert to a consistent form before combining.
Subtracting uncertainties when subtracting quantities.
Put it right: Absolute uncertainties always add, even for subtraction.

Exam tips

Write down the rule you are using before substituting numbers to avoid mixing rules.
Convert all uncertainties to the same type (absolute or percentage) before combining.
For powers, remember to multiply the percentage uncertainty by the exponent.
Check that the final uncertainty has the same units as the quantity if absolute, or is a percentage if percentage.

Try the lesson

The start of the Measurements and uncertainties: (c) absolute and percentage uncertainties when data are combined by addition, subtraction, multiplication, division and raising to powers lesson, made from checked teaching notes for this specification point.

Listen

When combining measurements, uncertainties propagate. For addition and subtraction, add absolute uncertainties: if z = x + y or z = x − y, then Δz = Δx + Δy. For multiplication and division, add percentage uncertainties: if z = xy or z = x/y, then %Δz = %Δx + %Δy. For powers, multiply the percentage uncertainty by the power: if z = xⁿ, then %Δz = n × %Δx. Absolute uncertainty is the uncertainty in the same units as the quantity; percentage uncertainty is (absolute uncertainty / value) × 100%. Always convert to the required form at the end. A strong answer earns marks for these points. For addition and subtraction, absolute uncertainties add. For multiplication and division, percentage uncertainties add. For raising to a power, percentage uncertainty is multiplied by the power. Percentage uncertainty = (absolute uncertainty / measured value) × 100%. Exam tip: Write down the rule you are using before substituting numbers to avoid mixing rules.

See it

A top-down flowchart. The top node 'Combining measurements' branches into three nodes: 'Addition or subtraction', 'Multiplication or division' and 'Raising to a power'. 'Addition or subtraction' leads to 'Add absolute uncertainties'. 'Multiplication or division' leads to 'Add percentage uncertainties'. 'Raising to a power' leads to 'Multiply percentage uncertainty by the power'. All three of these rule nodes then lead to a single final node, 'Convert to required form at the end'. — It shows which uncertainty rule applies to addition or subtraction, multiplication or division, and raising to a power, all ending in converting to the required form.

Label the diagram

Some boxes have lost their names. Pick the right name for each number.

The diagram again, with 3 boxes numbered instead of named. A top-down flowchart. The top node 'Combining measurements' branches into three nodes: 'Addition or subtraction', 'Multiplication or division' and 'Raising to a power'. 'Addition or subtraction' leads to 'Add absolute uncertainties'. 'Multiplication or division' leads to 'Add percentage uncertainties'. 'Raising to a power' leads to 'Multiply percentage uncertainty by the power'. All three of these rule nodes then lead to a single final node, 'Convert to required form at the end'.

1Box 1
2Box 2
3Box 3

0 of 3 labelled

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